Method of increasing tensile strength of aluminum castings

ABSTRACT

A multiple step method increases net tensile strengths of high pressure die cast (HPDC) aluminum components through an alloy- and process-dependent thermal treatment. The highest temperature feasible for solution treatment of an HPDC casting is determined by computational thermodynamics, kinetics and the gas laws based on the alloy composition and gas pressure in the finally solidified parts. Determining the maximum solution temperature involves mapping pressure in the bubbles of solidified material to avoid the formation of blisters by surface adjacent bubbles in the casting. To reduce residual tensile stress, the HPDC parts are air cooled after the solution treatment. Finally, a specific, multiple temperature aging cycle is utilized to improve the aging response of air cooled HPDC parts and increase net tensile strength.

FIELD

The present disclosure relates to high pressure aluminum die casting and more particularly to a method of increasing the tensile strength of high pressure aluminum alloy die castings.

BACKGROUND

The statements in this section merely provide background information related to the present disclosure and may or may not constitute prior art.

The high pressure die casting (HPDC) process is widely used for mass production of metal components because of low cost, close dimensional tolerances, i.e., near-net-shape, and smooth surface finish. Automotive industry manufacturers are increasingly required to utilize the high pressure die casting process to produce near-net-shape aluminum components with a combination of high tensile strength and ductility, because this process is the most economical method for high volume production. One disadvantage of the conventional HPDC process is that parts so produced are not amenable to solution treatment (T4) at high temperatures, for example 500° C., which significantly reduces the potential of precipitation hardening through a full T6 or T7 heat treatment.

This is due to the high quantity of porosity and voids in the finished HPDC components due to shrinkage during solidification and in particular the gases, such as air, hydrogen and or vapors formed from the decomposition of die lubricants during mold filling. It is almost impossible to find a conventional HPDC component without large, entrained gas bubbles. The internal pores containing gases or gas forming compounds in high pressure die castings expand during conventional solution treatment at elevated temperatures, resulting in the formation of surface blisters. The presence of these blisters affects not only the appearance of the castings but also dimensional stability and in particular the mechanical properties of the components.

Because of the potential blister problem, conventional HPDC aluminum components are most typically used in as-cast, or to a lesser extent, in aged conditions such as T5. Even with T5 aging, the increase of yield strength is very limited and sometimes there is no improvement because the concentrations of hardening solutes for artificial aging (T5) in typical as-cast HPDC parts are very low. As a result, the mechanical properties of HPDC aluminum parts are usually low for a given aluminum alloy in comparison with other casting processes because the aluminum parts made by other casting processes can be heat treated in full T6 and T7 conditions.

In T5 aging, there are three types of aging conditions that are commonly referred to as under aging, peak aging and over aging. At an initial stage of the aging, GP zones and fine shearable precipitates form and the structure is considered under aged. At this stage, the material hardness and yield strength are usually low. Increased time at a given temperature or aging at a higher temperature further evolves the precipitate structure and hardness and yield strength increase to a maximum, the peak aging/harness condition. Further aging decreases the hardness/yield strength and the structure becomes overaged due to precipitate coarsening and its transformation of crystallographic incoherency.

Considering that typical HPDC aluminum components inevitably contain entrapped air, any solution treatment needs to be specifically tailored to the quality of the casting, that is, the amount of entrapped air, and the alloy used. Any subsequent artificial aging (T5) is also a critical step to achieve the desired tensile properties without causing blister problems. The strengthening resulting from aging occurs because the solute taken into supersaturated solid solution forms precipitates which are finely dispersed throughout the grains and which increase the ability of the alloy to resist deformation by the process of slip and plastic flow. Maximum hardening or strengthening occurs when the aging treatment leads to the formation of a critical dispersion of at least one type of these fine precipitates.

Last of all, there exists a significant amount of residual stress in as-cast HPDC parts, particularly when the parts are quenched in water at room temperature after they are ejected from the die. High residual stress reduces the material net strength for structure loading.

SUMMARY

The present invention provides a multi-step method for increasing net tensile strength of HPDC aluminum components through an alloy- and process-dependent thermal treatment. The highest temperature feasible for solution treatment of an HPDC casting is determined by computational thermodynamics, kinetics and the gas laws based on the alloy composition and gas pressure in the finally solidified parts. Determining the maximum solution temperature involves mapping pressure in the bubbles of solidified material in order to avoid the formation of blisters by surface adjacent bubbles in the casting. To reduce residual tensile stress, the HPDC parts are air cooled after the solution treatment. A specific, multiple temperature aging cycle is utilized to improve the aging response of air cooled HPDC parts and to increase net tensile strength.

Thus it is an aspect of the present disclosure to provide a method for increasing net tensile strengths of HPDC aluminum components.

It is a further aspect of the present disclosure to provide a multi-step method for increasing net tensile strengths of HPDC aluminum components.

It is a still further aspect of the present disclosure to provide a multi-step method for increasing net tensile strengths of HPDC aluminum components through an alloy- and process-dependent thermal treatment.

It is a still further aspect of the present disclosure to provide a method for increasing net tensile strengths of HPDC aluminum components including the step of determining the highest temperature feasible for solution treatment of an HPDC casting.

It is a still further aspect of the present disclosure to provide a method for increasing net tensile strengths of HPDC aluminum components including the step of air cooling the component after solution treatment.

It is a still further aspect of the present disclosure to provide a method for increasing net tensile strengths of HPDC aluminum components including the step of utilizing a specific aging cycle to improve the aging response and maximize net tensile strength.

Further aspects, advantages and areas of applicability will become apparent from the description provided herein. It should be understood that the description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.

DRAWINGS

The drawings described herein are for illustration purposes only and are not intended to limit the scope of the present disclosure in any way.

FIG. 1 is a phase diagram of an A380 aluminum alloy as a function of Cu content;

FIG. 2 is a sequence of three views showing the evolution of a portion of an HPDC casting from solidification, through room temperature, to an elevated temperature;

FIG. 3 is a graph with three plots showing particle size on the ordinate (Y) axis and solution treatment time on the abscissa (X) axis;

FIG. 4 is a graph with multiple plots showing residual stress on the ordinate (Y) axis and several air and water quenched aluminum components on the abscissa (X) axis;

FIG. 5 is a graph with multiple plots showing yield strength on the ordinate (Y) axis and several aging treatments on the abscissa (X) axis;

FIG. 6 is a qualitative graph of the non-isothermal aging cycle according to the present disclosure for increasing the strength of an air quenched HPDC aluminum casting with temperature on the ordinate (Y) axis and time on the abscissa (X) axis; and

FIG. 7 is the multiple step aging cycle according to the present disclosure which reduces residual stress in aluminum casting of dissimilar materials with temperature on the ordinate (Y) axis and time on the abscissa (X) axis.

DETAILED DESCRIPTION

The following description is merely exemplary in nature and is not intended to limit the present disclosure, application, or uses.

With reference now to FIG. 1, a first portion and step of the method or process relates to the determination of the solution treatment (dissolution) temperature (T_(ST)). With solution treatment, the dissolution rate increases with temperature. The higher the solution treatment temperature, the faster the rate of element dissolution and spheroidization of undissolved constituents as well as the homogenization of solute concentrations in the metal or alloy. In practice, however, the solution treatment temperature cannot be higher than a critical temperature above which incipient blistering and melting occurs.

The metal or alloy incipient melting temperature is determined by the composition of the alloy and especially by its thermodynamic properties such as solidus. As utilized herein, the term solidus refers to a line or curve on a plot of temperature versus composition of an alloy below which the alloy is entirely solid. In solution treatment, the dissolution temperature cannot exceed solidus of any phases in the alloy microstructure. The heavy, solid line 10 in the phase diagram appearing as FIG. 1 shows the variation of solidus as a function of Cu content in a high pressure die casting aluminum alloy such as A380 alloy. For example, for an alloy containing between 3 and 4% Cu, the solution treatment temperature cannot exceed approximately 490° C.

Blister appearance is determined by the balance of pressure inside air bubbles and alloy strength at a given temperature. In general, the severity of blistering is increased significantly with an increase in temperature since both the pressure inside air bubbles increases and alloy strength decreases dramatically with temperature.

Referring now to FIG. 2, the evolution of entrapped air bubbles, one of which is illustrated in FIG. 2, from solidification which occurs under pressure during the die casting process, designated 20A, through cooling at room temperature (RT), designated 20B, to blistering at an elevated temperature (ET), designated 20C, is shown. Basically, the gas pressure inside the bubbles 20A, 20B and 20C and the volume of the bubble obeys the combined gas laws at the various temperatures. The actual volume of the bubbles 20A, 20B and 20C is balanced by either the alloy yield strength, externally applied pressure, or both. The following equation describes this activity:

$\frac{P_{solidus}V_{solidus}}{T_{solidus}} = {\frac{P_{RT}V_{RT}}{T_{RT}} = \frac{\sigma_{{ys}@{ST}}V_{ST}}{T_{ST}}}$

where P_(solidus) is the pressure inside the entrapped air bubble at solidus (MPa), V_(solidus) is the volume of the entrapped air bubble at solidus temperature (m̂3), T_(solidus) is the solidus temperature (° K), P_(RT) is the pressure inside the entrapped air bubble at room temperature (MPa), V_(RT) is the volume of the entrapped air bubble at room temperature (m̂3), T_(RT) is room temperature (° K), σ_(ys@ST) is the alloy yield strength at solution treatment temperature (MPa), V_(ST) is the volume of the entrapped air bubble 20C at the solution treatment temperature (m̂3) and T_(ST) is the solution treatment temperature (° K).

Upon solidifying, the aluminum surrounding the entrained air bubble is, of course, solid and thus the volume of the air bubble 20B is fixed and can be considered constant at room temperature.

The temperature dependence of material yield stress σ_(ys)(T) can be determined by linearly reducing the room temperature yield strength when temperature is lower than T_(min) and by adjusting the low temperature yield stress σ_(ys)(T_(min)) for the loss of stiffness that accompanies the increase in temperature.

${\sigma_{ys}(T)} = {{{\sigma_{ys}\left( T_{\min} \right)} + {{\left( {{\sigma_{ys}(298)} - {\sigma_{ys}\left( T_{\min} \right)}} \right)\left\lbrack \frac{T_{\min} - T}{T_{\min} - 298} \right\rbrack}\mspace{14mu} {when}\mspace{14mu} T}}<=T_{\min}}$ $\mspace{76mu} {{\sigma_{ys}(T)} = {{{{\sigma_{ys}\left( T_{\min} \right)}\left\lbrack {1 - {C_{ys}\left( \frac{E_{LT} - {E(T)}}{E_{LT}} \right)}} \right\rbrack}\mspace{14mu} {when}\mspace{14mu} T} > T_{\min}}}$

where

is an empirically determined proportionality constant (1.5˜2.0). σ_(ys)(T_(min))=(0.85˜0.9)σ_(yz)(298). The low temperature (T_(min)) is between 423˜453° K; The maximum temp (T_(max)) is between 673° and 723° K; T is the temperature (° K);

${E(T)} = {E_{2} - \frac{E_{LT} - E_{MT}}{1 + {\exp \left( \frac{T - t}{2} \right)}}}$ T^(*) = (T_(min) + T_(max))/2 ϕ = (T_(max) − T_(min))/4

where E(T) is the elastic modulus at temperature T (MPa); E_(LT) is elastic modulus at low temperature (T_(min)); E_(HT) is the elastic modulus at high temperature (T_(max)); E₀ is the elastic modulus at room temperature (73000˜77000 MPa); and σ_(ys)(298) is the material yield strength at room temperature.

  σ_(ys)(298) = σ? + Δσ?(t?T) + Δσ?(t?T) ?indicates text missing or illegible when filed

where t and T are aging times (seconds) and temperature (° K), respectively.

The contribution by solid solution hardening can be described by microstructure variables in terms of an equilibrium solute concentration at the aging temperature as shown below:

${{\Delta\sigma}_{ys}\left( {t,T} \right)} = \left\{ {{{\Delta\sigma}_{{ys}\; 0}^{\frac{3}{2}}(T)} + {{\exp \left( \frac{- t}{T_{t}(t)} \right)}\left\lbrack {{\Delta\sigma}_{{ys}\; 1}^{\frac{3}{2}} - {{\Delta\sigma}_{{ys}\; 0}^{\frac{3}{2}}(T)}} \right\rbrack}} \right\}^{\frac{2}{2}}$ where Δσ_(ys 1) = σ_(t) − σ_(l) Δτ_(ss 0)(T) = σ_(ys)(T) − σ_(l) ${\sigma_{ys}(T)} = {\sigma_{l} + {\left( {\sigma_{q} - \sigma_{l}} \right)\exp} - {\frac{2Q_{s}}{3R}\left( {\frac{1}{T} - \frac{1}{T_{s}}} \right)}}$ ${\tau_{1}(T)} = {K_{1}P_{v}T\; {\exp \left( \frac{Q_{o}}{RT} \right)}}$

The contribution to hardening by second phase precipitates is given by:

${{\Delta\sigma}_{ppt}\left( {t,T} \right)} = \frac{2{{S\left( {t,T} \right)}\left\lbrack {P^{*}\left( {t,T} \right)} \right\rbrack}^{\frac{1}{2}}}{1 + \left\lbrack {P^{*}\left( {t,T} \right)} \right\rbrack^{\frac{1}{2}}}$ ${P^{*}\left( {t,T} \right)} = \frac{P\left( {t,T} \right)}{P_{p}}$ ${P\left( {t,T} \right)} = {\frac{t}{T}\exp \left( \frac{- Q_{o}}{RT} \right)}$ ${S\left( {t,T} \right)^{2}} = {{\left( S_{0} \right)_{\max}^{0}\left\lbrack {1 - {\exp \frac{- Q_{s}}{R}\left( {\frac{1}{T} - \frac{1}{T_{s}}} \right)}} \right\rbrack}\left\lbrack {1 - {\exp \left( \frac{- t}{\tau_{1}(t)} \right)}} \right\rbrack}$

Table 1 shows several material constants for the yield strength models.

Yield Strength Model Parameters Cast aluminum alloys Intrinsic yield strength (MPa), σ_(i) 40~60 As-quenched yield strength (MPa), σ_(q) 70~90 Activation energy for aging (kJ/mol), Qa 180~230 Universal gas constant (J/mol. °K), R 8.314 Peak temperature-corrected time (s/°K), Pp 3.5E−22~3.5E−22 Metastable solvus temperature (°K), Ts 500~550 Max strength parameter at 0 K (MPa), (S₀)_(max) 240-280 Solvus enthalpy (kJ/mol), Qs 40~50 Constant relating τ1 to tp, K1 0.5~0.6

When there is no blistering, the volume of bubbles should be constant at the special solution temperature (V_(ST)), i.e., the V_(ST) should be equal to V_(solidus). So,

$T_{ST} = {{\frac{\sigma_{{ys}@{ST}}}{P_{solidus}}T_{solidus}} < T_{solidus}}$

where P_(solidus) is the pressure in the finally solidified bubble which can be determined by casting simulation. In a casting component like an engine block, the pressure in each entrained gas bubble can be mapped with respect to bubble location. Based on the mapped bubble pressure and material yield strength at elevated temperature, the feasible solution treatment temperature can be optimized.

A second portion and step of the method or process relates to the determination of the solution treatment time (t_(ST)). The solution treatment time, also called the dissolution time (t_(ST)), is based on the times for particles in the material or alloy to dissolve and the critical time at which the blister will begin to grow. The maximum solution treatment time (maximum dissolution time) should be below the time needed for particles to dissolve and below the critical time above which the entrained gas bubbles will grow.

-   -   t_(ST)=Min {dissolution time of Mg₂Si, Al₂Cu, critical         blistering growth time, etc.}

In solution treatment, the dissolution time for particles to dissolve follows Fick's second law.

$\frac{\partial C}{\partial t} = {F\frac{\partial^{2}C}{\partial x^{2}}}$ $D = {D_{0}{\exp \left( {- \frac{Q_{d}}{RT}} \right)}}$

where C is the alloy element content (at % or wt %), t is the time (seconds), x is the distance (meters); D is the diffusion coefficient (m̂2ŝ−1), D₀ is the diffusion constant (m̂2ŝ−1), R is universal gas constant (J/(mol. ° K)); T is the temperature (° K); and Q_(d) is the activation energy (J/mol).

FIG. 3 shows an example of the calculated dissolution times for different sizes of Mg₂Si particles in a cast aluminum alloy during solution treatment at 400° C. with particle size on the Y axis and solution treatment time on the X axis, beginning at 10 seconds. A first, lower curve 30A tracks dissolution of particle sizes of nominally 2.5 μm; a second, middle curve 30B tracks dissolution of particle size of nominally 5 μm; and the third, upper curve 30C tracks dissolution of particle size of nominally 10 μm. It is apparent from FIG. 3 that a much longer dissolution time is needed for complete dissolution of the larger particles.

As noted above, the solution treatment time (t_(ST)), is constrained by the critical time at which the blister will begin to grow. The critical blistering time depends upon how fast the material creeps. The creep strain rate is given by:

$\overset{.}{ɛ} = {\frac{d\; ɛ}{dt} = {A\; \sigma^{n}\sigma^{m}}}$

where ε is strain (dimension-less) and A, n and m are material parameters. A varies between 1×10̂−10 and 1×10̂−18, n is in the range of 1 through 10, m varies from −0.1 through 1.0 and a is the applied stress (MPa). In the bubble blistering process, σ=P_(ST)−σ_(ys)(ST), where P_(ST) is the gas pressure within the bubble at the solution treatment temperature, σ_(ys)(ST) is the material yield strength at the solution treatment temperature and t is the critical blistering time (seconds). As described above, the maximum solution treatment time (tsT) should be below the time needed for particles to dissolve and below the critical time above which the entrained gas bubbles will grow.

Referring now to FIG. 4, a comparison of residual stress in air and water quenched typical die castings, such as cylinder heads, is presented. The Y axis (ordinate) represents increasing residual stress, that is, maximum principal stress or MPa. Along the X axis (abscissa) are, to the left, three groups 40A, 40B and 40C of plots representing three different castings which have been air quenched. Within each group 40A, 40B and 40C, each of the three plots represents the stress at three different locations of each casting. To the right of FIG. 4 are six groups 42A, 42B, 42C, 42D, 42E and 42F of plots representing six different castings which have been water quenched. Within each group 42A, 42B, 42C, 42D, 42E and 42F each of the three plots represents the stress at three different locations within each casting. By reference and study of FIG. 4, it will be appreciated that, relative to a water quench, an air quench can significantly reduce residual stress, by at least 50 MPa, on average. Accordingly, a third portion and step of the method or process relates to the determination and utilization of an artificial aging step.

Referring now to FIG. 5, and notwithstanding the foregoing, it should be understood that an air quench usually results in both lower yield strength and ultimate tensile strength in comparison with water quench for the same aging condition. To make up for the loss of tensile strength due to air quenching, various step aging cycles are known to improve yield strength. FIG. 5 shows the improvement of yield strength of an air-quenched HPDC A380 alloy casting through different step aging cycles and, for purposes of comparison, one water quenched HPDC A380 alloy casting. The Y axis (ordinate) of FIG. 5 represents increasing yield strength (MPa). Along the X axis (abscissa) are five plots, the first plot 50A representing air cooling at room temperature; the second plot 50B representing air cooled and then held at 200° C. for 2 hours; the third plot 50C representing air cooled, then held at 95° C. for 2.5 hours and then held at 200° C. for 2 hours; the fourth plot 50D representing air cooled, then held at 95° C. for 2.5 hours, at 180° C. for 4 hours and then at 200° C. for 1 hour; and finally, the fifth plot 50E representing water quenched and then held at 200° C. for 2 hours.

As illustrated in FIG. 6, the non-isothermal scheme T(t) for an aluminum alloy can be optimized to achieve the desired yield and tensile strengths with minimum energy input, E(T,t) and aging time t. That is, and as the qualitative curve 60 of FIG. 6 illustrates, the temperature is first relatively rapidly increased to a maximum, then reduced and held at a lower temperature and finally slowly reduced. This multi-objective problem with constraints can be defined as:

$\left\{ {{\begin{matrix} {{\underset{{({T,t})} \in \Omega}{Min}{E\left( {T,t} \right)}} = {\underset{{({T,t})} \in \Omega}{Min}{\oint{{T(t)}{dt}}}}} \\ {{\underset{{({T,t})} \in \Omega}{Max}{{\Delta\sigma}_{ppt}\left( {T,t,C} \right)}}\mspace{104mu}} \end{matrix}\Omega} = {{\left\{ {{0 < T < T_{c}};{0 < t < \infty};{0 < C < C_{0}}} \right\} {{\Delta\sigma}_{ppt}\left( {T,t,C} \right)}} \geq {\Delta\sigma}_{target}}} \right.$

where E(T,t) is the energy input, which is the function of temperature (T) and time (t), Δσ_(ppt) (T, t, C) is the increase of material strength due to precipitate hardening, Δσ_(target) is the desired strength increase needed for air-quench aluminum casting, C₀ and C are initial and current content (at % or wt %) of a hardening alloy element in an aluminum matrix during the aging cycle and Tc is the critical upper limit of aging temperature (° K).

Referring now to FIG. 7, the process also comprehends use of a multiple step aging cycle, depicted by the plot 70, having a higher temperature 72 during the early portion of the aging cycle, followed by reduced temperature 74 during a latter portion of the aging cycle which reduces residual stress in aluminum die castings, particularly in components where there are dissimilar materials like aluminum surrounding the cast iron liners of an engine block.

Accordingly, from the foregoing, it will be appreciated that a multiple step method or process of treating high pressure aluminum die castings to maximize their net tensile strength and reduce residual stress comprehends the steps of determining the highest temperature and shortest feasible time for solution treatment of the casting(s) through computational thermodynamics, kinetics and the gas laws based upon the aluminum alloy composition and the gas pressure in the solidified parts. This aspect of determining the maximum solution temperature is achieved by mapping pressure in the bubbles of solidified material as it is important to avoid the formation of blisters by surface adjacent bubbles in the casting. After solution treatment, the parts are air cooled to reduce residual tensile stress. Finally, the parts are subjected to a non-isothermal or multiple step aging cycle which maximizes the net tensile strength.

The foregoing multiple step process or method has been found to improve net tensile strength by at least 50%, relieve residual casting stress by between 40% and 80% and, in parts with diverse material such as aluminum engine blocks with cast iron cylinder liners, eliminate liner cracking.

The description is merely exemplary in nature and variations that do not depart from the gist of the disclosure are intended to be, and are considered to be, within the scope of this disclosure. Such variations are not to be regarded as a departure from the spirit and scope of the present disclosure. 

What is claimed is:
 1. A method of improving net tensile strength of high pressure die cast aluminum alloy part, comprising the steps of: determining a highest temperature and a shortest time for solution treatment of a die cast aluminum alloy part by mapping pressure in bubbles of solidified aluminum alloy and utilizing pressure and volume gas laws, subjecting the die cast aluminum alloy part to solution treatment for the determined highest temperature and shortest time, air cooling the die cast aluminum alloy part to reduce residual tensile stress, and subjecting the die cast aluminum alloy part to a non-isothermal, multiple step aging cycle to improve net tensile strength.
 2. The method of claim 1 further including the step of determining a solidus temperature for the aluminum alloy die cast part.
 3. The method of claim 1 wherein the temperature and time of the solution treatment avoid blister formation.
 4. The method of claim 1 wherein the solution treatment time is below a time at which entrained gas bubbles will grow.
 5. The method of claim 1 wherein the mapping of pressure in bubbles utilizes the equation: $\frac{P_{solidus}V_{solidus}}{T_{solidus}} = {\frac{P_{RT}V_{RT}}{T_{RT}} = {\frac{\sigma_{{ys}@{ST}}V_{ST}}{T_{ST}}.}}$
 6. The method of claim 1 wherein the solution treatment time determination utilizes the equations: $\frac{\partial C}{\partial t} = {{F\frac{\partial^{2}C}{\partial x^{2}}\mspace{14mu} D} = {D_{0}{\exp \left( {- \frac{Q_{d}}{RT}} \right)}}}$ where C is the alloy element content (at % or wt %), t is the time (seconds), x is the distance (meters); D is the diffusion coefficient (m̂2ŝ−1), D₀ is the diffusion constant (m̂2ŝ−1), R is universal gas constant (J/(mol. ° K)); T is the temperature (° K); and Q_(d) is the activation energy (J/mol).
 7. The method of claim 1 wherein determining the non-isothermal, multiple step aging process utilizes the equations: $\left\{ {{\begin{matrix} {{\underset{{({T,t})} \in \Omega}{Min}{E\left( {T,t} \right)}} = {\underset{{({T,t})} \in \Omega}{Min}{\oint{{T(t)}{dt}}}}} \\ {{\underset{{({T,t})} \in \Omega}{Max}{{\Delta\sigma}_{ppt}\left( {T,t,C} \right)}}\mspace{104mu}} \end{matrix}\Omega} = {{\left\{ {{0 < T < T_{c}};{0 < t < \infty};{0 < C < C_{0}}} \right\} {{\Delta\sigma}_{ppt}\left( {T,t,C} \right)}} \geq {\Delta\sigma}_{target}}} \right.$ where E(T,t) is the energy input, which is the function of temperature (T) and time (t), Δσ_(ppt) (T, t,C) is the increase of material strength due to precipitate hardening, Δσ_(target) is the desired strength increase needed for air-quench aluminum casting, C₀ and C are initial and current content (at % or wt %) of a hardening alloy element in an aluminum matrix during the aging cycle and Tc is the critical upper limit of aging temperature (° K).
 8. A method of improving net tensile strength of a high pressure die cast metal alloy component, comprising the steps of: determining a highest temperature and a shortest time for solution treatment of a high pressure die cast component by mapping pressure in bubbles in the solidified, die cast component and utilizing computational thermodynamic properties and gas law equations, subjecting the die cast component to solution treatment for the determined highest temperature and time, air cooling the die cast component to reduce residual tensile stress, and subjecting the die cast component to a non-isothermal, multiple temperature aging process to improve its net tensile strength.
 9. The method of claim 8 further including the step of determining a solidus temperature for the die cast metal alloy component.
 10. The method of claim 8 wherein the temperature and time of the solution treatment avoid formation of blisters on a surface of the die cast metal alloy component.
 11. The method of claim 8 wherein the solution treatment time is shorter than a time at which entrained gas bubbles will grow
 12. The method of claim 8 wherein the mapping of pressure in bubbles utilizes the gas law equations: $\frac{P_{solidus}V_{solidus}}{T_{solidus}} = {\frac{P_{RT}V_{RT}}{T_{RT}} = {\frac{\sigma_{{ys}@{ST}}V_{ST}}{T_{ST}}.}}$
 13. The method of claim 8 wherein the solution treatment time determination utilizes the equations: $\frac{\partial C}{\partial t} = {{F\frac{\partial^{2}C}{\partial x^{2}}\mspace{14mu} D} = {D_{0}{\exp \left( {- \frac{Q_{d}}{RT}} \right)}}}$ where C is the alloy element content (at % or wt %), t is the time (seconds), x is the distance (meters); D is the diffusion coefficient (m̂2ŝ−1), D₀ is the diffusion constant (m̂2ŝ−1), R is universal gas constant (J/(mol. ° K)); T is the temperature (° K); and Q_(d) is the activation energy (J/mol).
 14. The method of claim 8 wherein determining the non-isothermal, multiple step aging process utilizes the equations: $\left\{ {{\begin{matrix} {{\underset{{({T,t})} \in \Omega}{Min}{E\left( {T,t} \right)}} = {\underset{{({T,t})} \in \Omega}{Min}{\oint{{T(t)}{dt}}}}} \\ {{\underset{{({T,t})} \in \Omega}{Max}{{\Delta\sigma}_{ppt}\left( {T,t,C} \right)}}\mspace{104mu}} \end{matrix}\Omega} = {{\left\{ {{0 < T < T_{c}};{0 < t < \infty};{0 < C < C_{0}}} \right\} {{\Delta\sigma}_{ppt}\left( {T,t,C} \right)}} \geq {\Delta\sigma}_{target}}} \right.$ where E(T,t) is the energy input, which is the function of temperature (T) and time (t), Δσ_(ppt) (T, t,C) is the increase of material strength due to precipitate hardening, Δσ_(target) is the desired strength increase needed for air-quench aluminum casting, C₀ and C are initial and current content (at % or wt %) of a hardening alloy element in an aluminum matrix during the aging cycle and Tc is the critical upper limit of aging temperature (° K).
 15. A method of improving net tensile strength of a high pressure die cast aluminum alloy component, comprising the steps of: determining a highest temperature and a shortest time for solution treatment of a high pressure die cast aluminum alloy component by mapping pressure in bubbles in the solidified, aluminum alloy die cast component and utilizing computational thermodynamics and gas laws, subjecting the die cast aluminum alloy component to a solution treatment for the determined highest temperature and time, subjecting the die cast aluminum alloy component to air cooling to reduce residual tensile stress, and subjecting the aluminum alloy component to a non-isothermal, multiple temperature aging cycle to improve net tensile strength.
 16. The method of claim 15 wherein said a high pressure die cast aluminum alloy component is an engine block.
 17. The method of claim 15 further including the step of determining a solidus temperature for the aluminum alloy.
 18. The method of claim 15 wherein the temperature and time of the solution treatment avoid formation of blisters.
 19. The method of claim 15 wherein the multiple temperature aging cycle utilizes at least a first, higher temperature and a second, lower temperature. 